Thanks for all the comments. The RX 350 is an SUV, so it has a hatch not a trunk. Checking for the light has been easy, and that has not been the issue.
The car lives in a heated garage most of the time and that is usually where it had the dead battery until we got the trickle charger.
We’ve read some posts on the “Club Lexus” web site that suggests disabling the “Smart Key” when the car is not going to be used for a long period of time (like when she is out of town for a week or longer). It appears this has happened with other Lexus models (also BMW’s and other electronically tripped out cars from what we have seen on the discussion boards). However, her manual does not discuss this or the location of the switch. Any thoughts?
And yes, gas is $4.47/gallon in her home town, $4.20 in Anchorage currently.